Winch­ester teen gets an A for ef­fort in ques­tion­ing math ex­hibit

He spot­ted what ini­tially ap­peared to be an er­ror in a decades-old dis­play

The Washington Post Sunday - - COMMUTER - BY MO­RIAH BALINGIT mo­riah.balingit@wash­post.com

The Mu­seum of Science in Bos­ton tal­lies 1.4 mil­lion vis­its a year. Many of those visi­tors tour the Math­e­mat­ica ex­hibit, a beloved if low-tech at­trac­tion in­stalled in 1981 that fea­tures sculp­tures, ac­tiv­i­ties and a dizzy­ing ar­ray of num­bers, sym­bols and equa­tions to ex­plain math­e­mat­i­cal con­cepts.

While en­grossed in the mu­seum’s of­fer­ings when he vis­ited in early June, Vir­ginia high schooler Joseph Rosen­feld spot­ted what he be­lieved to be an er­ror in an equa­tion, a de­vel­op­ment that grabbed head­lines, in­clud­ing in his home­town pa­per, the Winch­ester Star, the Bos­ton Globe and as far away as the Times of Is­rael. The 15-yearold math whiz said he saw a mi­nus sign where he be­lieved there should be a plus sign in an equa­tion re­lated to the golden ra­tio, a num­ber and a con­cept that has in­trigued math­e­ma­ti­cians since the age of Pythago­ras (or about 2,500 years ago).

“I was ex­cited. I was very happy that I found the mis­take,” said Joseph, who is tak­ing ad­vanced math and will take AP Cal­cu­lus as a sopho­more this com­ing school year. “It doesn’t hap­pen ev­ery day.”

Af­ter Joseph alerted the mu­seum, staffers there wrote him to thank him and said they would at­tempt to change it.

“Thank you for tak­ing the time to leave your feed­back af­ter your re­cent visit to the Mu­seum of Science, Bos­ton. You are right that the for­mula for the golden ra­tio is in­cor­rect. We will be chang­ing the — sign to a + sign on the three places it ap­pears if we can man­age to do it with­out dam­ag­ing the orig­i­nal,” wrote Alana Parkes, an ex­hibit con­tent devel­oper, in an e-mail to Joseph in mid-June.

But did the 15-year-old spot an er­ror that had eluded mil­lions of visi­tors and the math­e­ma­ti­cian de­sign­ers of the ex­hibit, which had been on public dis­play for more than three decades? Well, not ex­actly. Upon fur­ther ex­am­i­na­tion, it turned out that both Joseph and the mu­seum’s ex­hibit were cor­rect.

The mu­seum has since re­tracted the orig­i­nal ad­mis­sion to the er­ror. As it turns out, the ex­hibit was dis­play­ing the equa­tion for the lesser-known sib­ling of the golden ra­tio — its re­cip­ro­cal, also known as the golden ra­tio con­ju­gate.

Eve Tor­rence, am­ath pro­fes­sor at Ran­dolph-Ma­con Col­lege, was shown a photo of the ex­hibit and said the mu­seum’s math checks out, even though it’s an un­usual way to talk about the con­cept.

“I’d call it un­com­mon, not the way most peo­ple think of the golden ra­tio nowa­days,” Tor­rence said. “It’s not what most peo­ple think of, but it’s not in­cor­rect.”

The golden ra­tio can be seen in what is known as a “golden rec­tan­gle”: When the sides of a rec­tan­gle are such that if you cut the rec­tan­gle in two us­ing the shorter side to make a square — and then dis­card the square — you end up with a sec­ond, smaller rec­tan­gle of equal pro­por­tions to the orig­i­nal rec­tan­gle. The process can be re­peated an in­fi­nite num­ber of times.

The golden ra­tio can be found in the ge­om­e­try of per­fectly drawn pen­ta­grams and pen­ta­gons and even in na­ture: the seeds in the cen­ter of sun­flow­ers and the scales of pine cones ar­range them­selves roughly ac­cord­ing to the golden ra­tio. The ra­tio is roughly equal to 1.62 and is rep­re­sented by the low­er­case Greek let­ter phi. Tor­rence said the con­stant has taken on a sort of mythol­ogy, with some claim­ing it can be found in the ge­om­e­try of the per­fect hu­man face. (“Silli­ness,” she quipped.)

The Math­e­mat­ica ex­hibit talks about “golden pro­por­tions.” In the equa­tion in ques­tion, the ex­hibit de­sign­ers took the ra­tio of the short side of a rec­tan­gle to the long side of the rec­tan­gle. That’s why the equa­tion the plac­ard dis­played con­tained a mi­nus sign where there would nor­mally be a plus sign. The re­cip­ro­cal is rep­re­sented by the uppercase phi.

Still, Tor­rence said she was im­pressed that Joseph spot­ted the dis­crep­ancy.

“I’m proud of him for notic­ing that it had a mi­nus sign in­stead of a plus sign, but it’s not tech­ni­cally wrong,” Tor­rence said. “He’s to be com­mended for ques­tion­ing au­thor­ity.”

Joseph said he was dis­ap­pointed when he found out that he had not ac­tu­ally found an er­ror. But he’s been en­joy­ing the media at­ten­tion. Thurs­day, he trav­eled to the Fox net­work’s stu­dio in Washington to ap­pear on “Fox & Friends.”

“Even though it wasn’t a mis­take, I’m get­ting a lot of pub­lic­ity,” Joseph said. “It can’t hurt with col­leges.”

It also will give Joseph a chance to re­turn to Bos­ton: Joseph’s fa­ther, Scott, said Fri­day that John Henry — prin­ci­pal owner of the Bos­ton Globe and the Bos­ton Red Sox— has in­vited the fam­ily to a Red Sox game at Fen­way Park.

The or­ga­ni­za­tion that rep­re­sents Charles and Ray Eames, the late de­sign­ers be­hind the ex­hibit, has also reached out telling the fam­ily that it is “im­pressed with Joseph’s find­ings.”

The Mu­seum of Science in Bos­ton has in­vited him back for a spe­cial tour of a new ex­hibit on the science and math be­hind Pixar films. Even af­ter back­track­ing on the er­ror, the mu­seum re­leased a state­ment com­mend­ing the teen for spot­ting the dif­fer­ence:

“The Mu­seum of Science is thrilled at Han­d­ley High School sopho­more Joseph Rosen­feld’s en­thu­si­asm about math and our Math­e­mat­ica ex­hibit. And it’s not at all sur­pris­ing that this en­ter­pris­ing stu­dent no­ticed the mi­nus signs be­cause the way the Mu­seum presents the golden ra­tio in its ex­hibit is in fact the less com­mon — but no less ac­cu­rate — way to present it. It’s ex­cit­ing that peo­ple around the coun­try are talk­ing about math and science and that, in the process, we learned some­thing too. Let’s hear it for STEM ed­u­ca­tion and for Joseph Rosen­feld!”

JEFF TAY­LOR/AS­SO­CI­ATED PRESS

Joseph Rosen­feld out­side John Han­d­ley High School, where he will be a sopho­more in the fall.

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